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Re: least squares method for determining a fix
From: Paul Werner
Date: 2003 Oct 10, 16:14 +0200
From: Paul Werner
Date: 2003 Oct 10, 16:14 +0200
Federico
Don't know if it is of any help but you can try
it
Paul
----- Original Message -----From: Federico RossiSent: Friday, October 10, 2003 1:39 PMSubject: least squares method for determining a fixHi,does anybody know the formulas to calculate the error ellipse around the fix obtained with the least squares method?I've got some formulas that I found on a Spanish site, but they don't explain what is sigma (I suppose a variance) and most of all how to compute it.The formulas are (a probability of 0.95 is generally considered):k=sqrt(-2*log(1-probability)theta=arctan(2*B/(A-C)a=sigma*k/sqrt(nObs/2+B/sin(theta))b=sigma*k/sqrt(nObs/2-B/sin(theta))where: a and b are the axis of the ellipsenObs is the number of sightsA, B and C are parameters calculated with the least squares method as found in the Nautical AlmanacThese formulas only give a and b, what about the orientation of the two axis?Thanks.Federico